We deny the validity of multiple polls, over a number of years, that show very high public support for background checks. And we are deluding ourselves.

This is the thing that shows the underlying fallacy of their approach. We still live in a country with a bicameral legislature and a clear separation of powers. Why? So that the majority can't run roughshod over the minority. The Founders would be appalled at the idea that contemporary public opinion would be allowed to override constitutional limits on power.

We are not, and should not be, governed by polls. Even if the 90% myth had a bit of truth to it (and we had a recent thread refuting that), it should not be allowed to have significant influence over lawmaking in the short term.